An Extend connection is used to indicate that an element extends the behavior of another. Extensions are used in Use Case models to indicate that one  Use Case (optionally) extends the behavior of another. An extending Use Case often expresses alternative flows.

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OMG UML Specification

The OMG UML specification (UML Superstructure Specification, v2.1.1, p. 587) states:

This relationship specifies that the behavior of a Use Case may be extended by the behavior of another (usually supplementary) Use Case. The extension takes place at one or more specific extension points defined in the extended Use Case. Note, however, that the extended Use Case is defined independently of the extending Use Case and is meaningful independently of the extending Use Case. On the other hand, the extending Use Case typically defines behavior that may not necessarily be meaningful by itself. Instead, the extending Use Case defines a set of modular behavior increments that augment an execution of the extended Use Case under specific conditions.

Note that the same extending Use Case can extend more than one Use Case. Furthermore, an extending Use Case may itself be extended.